Analysis Of Planar Multibody Systems Research Articles

Kinematics and dynamics of planar multibody systems with fully Cartesian coordinates and a generic rigid body

This work describes in detail the theoretical basis of the fully Cartesian coordinates formulation with a generic rigid body and evaluates its performance in the dynamic analysis of planar multibody systems. The topological features of the generic rigid body and the most relevant kinematic constraint equations are presented, aiming its application in the dynamic analysis of complex multibody systems and in advanced teaching.Contrarily to natural coordinates, in which the present formulation lays its foundation, planar rigid bodies are defined with a predetermined kinematic structure that resorts only to the Cartesian coordinates of one point and one unit vector. The introduction of the generic rigid body systematizes the discretization of the multibody system, simplifies the kinematic constraints required for its description, and renders higher physical meaning and sparsity to its mass matrix. However, it also slightly increases the number of generalized coordinates and kinematic constraints, required to model the multibody system, when compared to other global formulations.The present formulation was applied to the analysis of four planar models with different complexity levels, namely the slider-crank, double four-bar linkage, Jansen mechanism and a biomechanical model of the human body, presenting high agreement scores with benchmark and literature data.

Effect of novel continuous friction model on nonlinear dynamics of the mechanisms with clearance joint

A general methodology for the dynamic modelling and analysis of planar multi-body systems with a continuous friction model in joint clearance is presented. Joint clearance is the critical factor that influences the dynamic response and the performance of mechanisms for high-speed application. In light of recent developments in the joint clearance studies, the number of contact force models has been introduced with ignoring friction continuity. The selection of an appropriate continuous friction model is still challenging and essential, which requires further development. Therefore, a perfect continuous friction model, including the Stribeck effect, static, dynamic and viscous friction terms, is proposed and validated. Investigating the dynamic modelling and analysis of double rocker four-bar linkage mechanisms with frictional revolute clearance joints is presented to investigate friction models' effect when surfaces collide with a non-zero tangential velocity. Unlike the smooth crank input mechanism, a double rocker four-bar linkage mechanism is analysed as a challenging problem in the impact mode. Resolving this concern, the novel friction model avoids discontinuity at zero velocity considering the accurate static friction zone. The results reveal that the novel friction model, compared with the piecewise friction model, is more effective in reflecting the mechanical systems' dynamic behaviour. In order to grasp the nonlinear characteristics of the high-speed four-bar linkage mechanism with our model in joint clearance, the Poincaré portrait, and Fast Fourier transformation plot are employed. It is proved that chaos exists in the dynamic response with the influence of the restitution coefficients and kinetic coefficient of friction.

Dynamic Analysis of Planar Multibody Systems Considering Contact Characteristics of Ball Bearing Joint

A comparative study of dynamic analysis for planar multibody systems with ball bearing joints is conducted in this study. The transmission mechanism is used as the exemplar case for illustrating the effect of ball bearing joints on the dynamic behavior of multibody systems. To reflect the energy loss, the models of continuous contact force and modified Coulomb’s friction are considered in the kinematic equations for the multibody system with ball bearing joint. With this, the dynamic characteristics of the mechanism are studied. Meanwhile, an experimental platform is built to generate the test data for demonstrating the effectiveness and correctness of the proposed method. Moreover, the effects of driving speed and clearance size on the dynamic behavior of the multibody system are investigated. The numerical results indicate that the dynamic behavior of the mechanical system is sensitive to the variation of the design parameters and the selection of parameters can affect greatly the accuracy of the mechanism with clearance joints.

An approach for dynamic analysis of planar multibody systems with revolute clearance joints

Clearance is inevitable for manufacture and assembly in the revolute joints of multibody systems. Excessive value of joint clearance will lead to the poor dynamic performance of mechanism, namely noise, vibration and fatigue failure. This paper presents the development of a dynamic model for planar multibody systems with clearance joints. Based on the continuous contact law, the contact force model proposed by Lankarani and Nikravesh is employed to describe the contact–impact phenomenon between pin and hole. And, the incorporation of the friction influence on revolute joint clearance is conducted by a modified friction force model. According to the geometric relationship between contact elements, the kinematics of the multibody systems is mapped into the global coordinate systems. Additionally, an experimental test platform is set up whereby a slider–crank mechanism with two clearance joints is used as an example to demonstrate the correctness and effectiveness of the proposed approach. Finally, the effects of joint clearance on the dynamic characteristics of planar multibody systems are investigated.

On the use of two-dimensional Euler parameters for the dynamic simulation of planar rigid multibody systems

This paper introduces a new coordinate formulation for the kinematic and dynamic analysis of planar multibody systems composed of rigid bodies. The methodology presented in this work is called planar reference point coordinate formulation (RPCF) with Euler parameters. In the planar RPCF with Euler parameters, the rotational coordinates used for describing the body orientation are the redundant components of a two-dimensional unit quaternion that identify a planar set of Euler parameters. It is shown in the paper that the planar RPCF with Euler parameters allows for obtaining consistent kinematic and dynamic descriptions of two-dimensional rigid bodies. In the numerical solution of the equations of motion, the well-known generalized coordinate partitioning method can be effectively utilized to stabilize the violation of the algebraic constraints at the position and velocity levels leading to physically correct and numerically stable dynamic simulations. Furthermore, a standard numerical integration procedure can be employed for calculating an approximate solution of the equations of motion resulting from the planar RPCF with Euler parameters. In the paper, the computer implementation of the proposed formulation approach is demonstrated considering four rigid multibody systems which serve as simple benchmark problems.

A new numerical method for planar multibody system with mixed lubricated revolute joint

A new method for modeling and analysis of planar multibody systems with lubricated revolute joints is presented. This method is established by coupling the lubrication model of lubricated revolute clearance joint with the dynamics model of multibody system. The lubrication model is solved by the Finite Element Method, while the multibody dynamics equations are established by Lagrange's method. In order to take into account the effects of the surfaces roughness on the hydrodynamic lubrication when the oil film between the mating surfaces has a very small thickness, the average Reynolds equation is adopted. The hydrodynamic forces built up by the lubricant fluid are evaluated from the knowledge of the system variables and then included into the dynamics equations of the multibody system. In the end, the proposed approach is applied to the piston–connecting rod–crank system in a four-stoke gasoline engine with lubricated clearance joint at the big end of the connecting rod. The clearance size and lubricant viscosity are investigated so as to reveal their influences on both the dynamics and lubrication performances. From the main obtained results, it can be concluded that the use of lubricant at mechanism joints is an effective way to ensure better performance. Within a given range, the cases with smaller clearance or higher lubricant viscosity are conducive to maintaining the stability of the motion of mechanism, and will decrease the friction power loss.

Computational structural analysis of planar multibody systems with lower and higher kinematic pairs

Abstrac Kinematic and dynamic modeling of multibody systems requires an initial stage of topological recognition or structural analysis, in which the analyst must identify the model coordinates and a sufficient number of constraint equations to relate them. This initial phase could be solved quickly, safely and automatically, determining the kinematic structure of the multibody system; that is, dividing it into a set of kinematic chains called structural groups. Furthermore, structural groups are widely used for structural synthesis and so, the analysis and design of multibody systems can be integrated into the same software package. On the basis of known graph-analytical methods for structural analysis, a computational method that determines the kinematic structure of a multibody system from its adjacency matrix is developed and evaluated. This method allows the choosing of any type of coordinates (relative, natural or reference point) and the kinematic and dynamic formulations most appropriate for solving the problem. The algorithm has been applied to a large number of mechanical systems of different complexity, offering the same kinematic structure as was obtained through the application of graph-analytical methods.

Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance

A general methodology for dynamic modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance is presented in this paper. The bearing joint has been modeled by introducing a nonlinear constraint force system, which takes into account the contact stiffness interaction between the rolling elements and the raceways. The evaluation of the contact forces is based on the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. The proposed model has been applied in the dynamic simulations of a planar slider–crank mechanism with a deep groove ball bearing joint. By numerical calculation, the variations of the bearing eccentric trajectory, the contact force on each ball element, the equivalent joint constraint force and the crank moment are discussed. The results indicate that the effects of the bearing clearance and flexibility on the dynamic performance of high-speed mechanisms cannot be ignored. The present methodology can not only be used to analyze the overall dynamic behavior of multibody systems with the deep groove ball bearing, but also to obtain the dynamic load on each ball element in bearing. Furthermore, the simulations of the dynamic loads on ball elements can be used for the strength checking, fatigue life prediction and wear analysis of the deep groove ball bearing in multibody systems.

Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints

In this paper, the dynamic response of a planar rigid multi-body system with stick–slip friction in revolute clearance joints is studied. LuGre friction law is proposed to model the stick–slip friction at the revolute clearance joints. This is because using this law, one can capture the variation of the friction force with slip velocity, thus making it suitable for studies involving stick–slip motions. The effective coefficient of friction is represented as a function of the relative tangential velocity of the contacting bodies, that is, the journal and the bearing, and an internal state. In LuGre friction model, the internal state is considered to be the average bristle deflection of the contacting bodies. By applying the LuGre friction law on a typical slider–crank mechanism, the friction force in the revolute joint having clearance is seen not to have a discontinuity at zero slip velocity throughout the simulation unlike in static friction models. In addition, LuGre model was observed to capture the Stribeck effect which is a phenomenon associated directly with stick–slip friction. The friction forces are seen to increase with increase in input speed. The effect of stick–slip friction on the overall dynamic behavior of a mechanical system at different speeds was seen to vary from one clearance joint to another.

Dynamic Response of Multibody Systems with Multiple Clearance Joints

A general methodology for the dynamic modeling and analysis of planar multibody systems with multiple clearance joints is presented. The inter-connecting bodies that constitute a real physical mechanical joint are modeled as colliding components, whose dynamic behavior is influenced by the geometric, physical and mechanical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory, together with a dissipative term associated with the internal damping, is utilized to evaluate the intra-joint normal contact forces. The incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also included in this study. The suitable contact force models are embedded into the dynamic equations of motion for the multibody systems. In the sequel of this process, the fundamental methods to deal with contact-impact events in mechanical systems are presented. Finally, two planar mechanisms with multiple revolute clearance joints are used to demonstrate the accuracy and efficiency of the presented approach and to discuss the main assumptions and procedures adopted. The effects of single versus multiple clearance revolute joints are discussed.

The effect of the lubricated revolute joint parameters and hydrodynamic force models on the dynamic response of planar multibody systems

In this work a comprehensive methodology for dynamic modeling and analysis of planar multibody systems with lubricated revolute joints is presented. In general, this type of mechanical systems includes journal-bearings in which the load varies in both magnitude and direction. The fundamental issues associated with the theory of lubrication for dynamically loaded journal-bearings are revisited that allow for the evaluation of the Reynolds equation for dynamic regime. This approach permits the derivation of the suitable hydrodynamic force laws that are embedded into the dynamics of multibody systems formulation. In this work, three different hydrodynamic force models are considered, namely the Pinkus and Sternlicht approach for long journal-bearings and the Frêne et al. models for both long and short journal-bearings. Results for a planar slider–crank mechanism with a lubricated revolute joint between the connecting-rod and slider are presented and utilized to discuss the assumptions and procedures adopted throughout the present study. Different test scenarios are taken into account with the purpose of performing a comparative study for quantifying the effect of the clearance size, lubricant viscosity, input crank speed and hydrodynamic force model on the dynamic response of multibody systems with lubricated revolute joints. From the global results obtained from computational simulations, it can be concluded that the clearance size, the lubricant viscosity and the operating conditions play a key role in predicting the dynamic behavior of multibody systems.

Analysis of planar multibody systems with revolute joint wear

Wear prediction on the components of a mechanical system without considering the system as a whole will, in most cases, lead to inaccurate predictions. This is because the wear is directly affected by the system dynamics which evolves simultaneously with the wear. In addition, the contact condition (regions of contact for the wearing bodies) also depends on the system dynamics and can only be determined in a multibody dynamics framework. In this work, a procedure to analyze planar multibody systems in which wear is present at one or more revolute joints is presented. The analysis involves modeling multibody systems with revolute joints that consist of clearance. Wear can then be incorporated into the system dynamic analysis by allowing the size and shape of the clearance to evolve as dictated by wear. An iterative wear prediction procedure based on Archard's wear model is used to compute the wear as a function of the evolving dynamics and tribological data. The procedure is then validated by comparing the wear prediction with wear on an experimental slider-crank mechanism.

Dynamic Analysis for Planar Multibody Mechanical Systems with Lubricated Joints

The dynamic analysis of planar multibody systems with revolute clearance joints, including dry contact and lubrication effects is presented here. The clearances are always present in the kinematic joints. They are known to be the sources for impact forces, which ultimately result in wear and tear of the joints. A joint with clearance is included in the multibody system much like a revolute joint. If there is no lubricant in the joint, impacts occur in the system and the corresponding impulsive forces are transmitted throughout the multibody system. These impacts and the eventual continuous contact are described here by a force model that accounts for the geometric and material characteristics of the journal and bearing. In most of the machines and mechanisms, the joints are designed to operate with some lubricant fluid. The high pressures generated in the lubricant fluid act to keep the journal and the bearing surfaces apart. Moreover, the lubricant provides protection against wear and tear. The equations governing the dynamical behavior of the general mechanical systems incorporate the impact force due to the joint clearance without lubricant, as well as the hydrodynamic forces owing to the lubrication effect. A continuous contact model provides the intra-joint impact forces. The friction effects due to the contact in the joints are also represented. In addition, a general methodology for modeling lubricated revolute joints in multibody mechanical systems is also presented. Results for a slider-crank mechanism with a revolute clearance joint between the connecting rod and the slider are presented and used to discuss the assumptions and procedures adopted.